Hassan Ymeri

Fast and accurate analysis of the multiconductor interconnects

Abstract This paper describes a fast and accurate semi-analytical procedure for determining capacitance and inductance of multilayer structures with multiple conductors in the top layer (with zero and non-zero conductor thickness). The technique uses the quasi-analytic electrostatic Green’s function of multilayer structures, which is integrated to a series expansion valid for uniform charge distributions. Computed results are given for some cases to show the advantages and simplicity of our procedure as compared to the methods available in the literature.

New analytic expressions for mutual inductance and resistance of coupled interconnects on lossy silicon substrate

A new analytic model for series mutual impedance of coupled interconnects on lossy silicon substrate is presented. The model includes the frequency-dependent distribution of the current on the silicon substrate (the substrate skin effect). From this model, simple formulas for accurate calculation of the frequency dependent distributed mutual inductance and the associated series mutual resistance of coupled interconnects on a silicon substrate are derived. The validity of the proposed formulas has been checked by comparison with equivalent circuit model data and corresponding full wave solutions. Through this work, it is found that the effect of the semiconducting substrate return path on the transmission behaviour of the interconnects must be well modeled for accurate prediction of the resistance and inductance over the whole frequency range.

Computation of capacitance matrix for integrated circuit interconnects using semi-analytic Green's function method

In this paper a method for computing the capacitance matrix of a multiconductor interconnect line in a multilayered dielectric region is presented. The number of conductors and dielectric layers are arbitrary. The conductors are infinitesimally thin, and can be placed anywhere in the structure. The formulation is obtained by using a semi-analytic Greens function for multilayer structures, which is integrated to a series expansion, valid for uniform charge distribution on the conductors. In addition, the quasi-analytical evaluation of the entries of the Galerkin matrix leads to a very efficient and accurate computer code. Computed results are given for some cases of the integrated circuit interconnects to show the advantages and simplicity of our procedure as compared to the methods available in the literature.

On the modelling of multiconductor multilayer systems for interconnect applications

In this paper, a new quasi-TEM capacitance and inductance analysis of multiconductor multilayer interconnects is successfully demonstrated by using the dielectric Greens function and boundary integral equation approach. Presented is the case with an arbitrary number of dielectric layers and with zero-thickness conductors in the upper most layer. Since the method has been developed for application on microelectronic interconnect structures, we use the Galerkin method for constant charge distribution on the conductors to generate the numerical results. Since the silicon substrate has a substantial effect on the inductance parameter, it is taken into account to determine the transmission line parameters. Studies conducted here show that ignoring the silicon substrate leads to erroneous results in estimating the inductance parameter of the structure. Since the procedure is very efficient as well as accurate, it will be a very useful tool in the practical calculations for high-speed and high-density IC signal integrity verification.

Accurate analytic expressions for frequency-dependent inductance and resistance of single on-chip interconnects on conductive silicon substrate

Simple and accurate closed-form expressions to calculate frequency-dependent distributed inductance and associated distributed series resistance per-unit-length of single on-chip interconnects on a lossy silicon substrate are presented. The analytic formulas for the frequency-dependent series impedance parameters are obtained using a closed-form integration method and the vector magnetic potential equation. It is shown that the calculated frequency-dependent inductance L(f) and resistance R(f) per-unit-length are in good agreement with the results obtained from rigorous full wave solutions and CAD-oriented equivalent-circuit modeling approach.

New closed-form formula for frequency-dependent resistance and inductance of IC interconnects on silicon substrate

A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations needed to obtain the desired expressions. As a result, for the first time, we present a new, simple, yet surprisingly accurate, closed-form expression which yields accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulae describe the mutual line impedance behaviour over the whole frequency range (i.e. also in the transition region between the skin effect, slow-wave and dielectric quasi-TEM modes). The results have been compared with reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.

New modeling approach of on‐chip interconnects for RF integrated circuits in CMOS technology

New analytical approximation for the frequency‐dependent impedance matrix components of symmetric VLSI interconnect on lossy silicon substrate are derived. The results have been obtained by using an approximate quasi‐magnetostatic analysis of symmetric coupled microstrip on‐chip interconnects on silicon. We assume that the magnetostatic field meets the boundary conditions of a single isolated infinite line; therefore, the boundary conditions for the conductors in the structure are approximately satisfied. The derivation is based on the approximate solution of quasi‐magnetostatic equations in the structure (dielectric and silicon semi‐space), and takes into account the substrate skin‐effect. Comparisons with published data from circuit modeling or full‐wave numerical analyses are presented to validate the inductance and resistance expressions derived for symmetric coupled VLSI interconnects. The analytical characterization presented in this paper is well situated for inclusion into CAD codes in the design of RF and mixed‐signal integrated circuits on silicon.

On the mutual capacitance and inductance of a shielded interconnect four-line system

In this paper, the capacitance and inductance of a four-line transmission structure is characterized. The procedure used was developed by Ymeri et al for general analysis of multilayer multiconductor interconnects for specific applications in microelectronics. The characterization is based on the determination of the quasi-static electric scalar potential in the structure making up the four-line interconnect. Using the electric potential, the mutual capacitances and inductances are found. The characterization of the four-conductor structure is significantly different from the simple conductor pair because the symmetry of the pair is lost. A number of numerical results are calculated and presented.

Frequency-dependent mutual resistance and inductance formulas for coupled IC interconnects on an Si-SiO2 substrate

Abstract A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of a lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations which are needed in obtaining the desired expressions. As a result, for the first time, we present a new simple, yet surprisingly accurate closed-form expression which yield accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulas describe the mutual line impedance behaviour over the whole frequency range ( i.e. also in the transition region between the skin effect, slow wave, and dielectric quasi-TEM modes). The results have been compared with the reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.

Admittance matrix calculations of on-chip interconnects on lossy silicon substrate using multilayer Green's function

In this paper, a simple method for computation of the shunt admittance matrix of multiconductor interconnects on a general lossy multilayer substrate at high bit rates is presented. The analysis is based on the semi-analytical Greens function approach and the recurrence relation between the coefficients of potential in n and n+1 layers. The electromagnetic concept of free charge density is applied. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the method of moments. The new approach is especially suited to modeling 2D layered structures with planar boundaries for frequencies up to 20 GHz (quasi-stationary field approach). The transmission line parameters (capacitance and conductance per unit length) for the given interconnect multilayer geometry are computed. A discussion of the calculated line admittance matrix in terms of technological and geometrical parameters of the structure is given. A comparison of the numerical results from the new procedure with the techniques presented in the previous publications are also provided.